What is the answer to log_{x+6}(3x^2+6x)=2 ?

The answer to log_{x+6}(3x^2+6x)=2 is x=-3,x=6

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log_{x+6}(3x^2+6x)=2

lo g_{x + 6} (3 x^{2} + 6 x) = 2

x = - 3, x = 6

Solution steps

lo g_{x + 6} (3 x^{2} + 6 x) = 2

Apply log rules

\frac{ln ( 3 x ^{2} + 6 x )}{ln ( x + 6 )} = 2

Multiply both sides by

ln (x + 6)

\frac{ln ( 3 x ^{2} + 6 x )}{ln ( x + 6 )} ln (x + 6) = 2 ln (x + 6)

Simplify

ln (3 x^{2} + 6 x) = 2 ln (x + 6)

Apply log rules

3 x^{2} + 6 x = (x + 6)^{2}

Solve

3 x^{2} + 6 x = (x + 6)^{2} : x = - 3, x = 6

x = - 3, x = 6

Verify Solutions:

x = - 3

True

, x = 6

True

The solutions are

x = - 3, x = 6

ln (4 - x) = 0

ln (x + 6) = - 1

lo g_{a} (n^{a}) = n

ln (x + 3) - ln (x) = ln (6)

lo g_{3} (x) = 3 + 2 lo g_{x} (9)

What is the answer to log_{x+6}(3x^2+6x)=2 ?
The answer to log_{x+6}(3x^2+6x)=2 is x=-3,x=6
Solve for x: log_{x+6}(3x^2+6x)=2
The solution is x=-3,x=6